package com.ma.dp.a01;

import java.util.Arrays;

/**
 * @ClassName Solution64
 * @Author: mayongqiang
 * @DATE 2022/4/11 10:42
 * @Description: 最小路径和
 */
public class Solution64 {
    /*
    给定一个包含非负整数的 m x n 网格 grid ，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。说明：每次只能向下或者向右移动一步。
        输入：grid = [[1,3,1],[1,5,1],[4,2,1]]  输出：7
        解释：因为路径 1→3→1→1→1 的总和最小
     */
    public static void main(String[] args) {
        int[][] grid = new int[][]{{1, 3, 1}, {1, 5, 1}, {4, 2, 1}};
        System.out.println(minPathSum02(grid));

    }

    /*
        trans:  dp[i][j] = Math.min(dp[i-1][j],dp[i][j-1]);
        target: dp[m-1][n-1]
     */
    static int[][] memo;

    public static int minPathSum01(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        memo = new int[m][n];
        for (int[] row : memo) {
            Arrays.fill(row, -1);
        }
        return dp(grid, m - 1, n - 1);
    }

    private static int dp(int[][] grid, int i, int j) {
        if (i == 0 && j == 0) {
            return grid[0][0];
        }
        if (i < 0 || j < 0) {
            return Integer.MAX_VALUE;
        }
        if (memo[i][j] != -1) {
            return memo[i][j];
        }
        memo[i][j] = grid[i][j] + Math.min(dp(grid, i - 1, j), dp(grid, i, j - 1));
        return memo[i][j];
    }

    static int minPathSum02(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];
        for (int i = 1; i < m; i++) {
            dp[i][0] = grid[i][0] + dp[i - 1][0];
        }
        for (int j = 1; j < n; j++) {
            dp[0][j] = grid[0][j] + dp[0][j - 1];
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j] = grid[i][j] + Math.min(dp[i - 1][j], dp[i][j - 1]);
            }
        }
        return dp[m-1][n-1];
    }
}
